How does current affect electric potential?

[Apteronotus]

Suppose you have an two objects A and B having different potentials \phi_A, \phi_B and voltage V=\phi_A- \phi_B.

Suppose you allow current to flow from one object to another for some period of time according to Ohm's Law (V=IR)
Now what is the new value of the voltage?

thanks

 

[vin300]

That depends on the rate of electrochemical reaction in the cell

 

[Stonebridge]

What are the objects A and B?
As you have defined V as the pd between the two objects, then it is perfectly feasible that the flow of charge is such that the pd between A and B becomes zero after a time t.
I think you need to be more specific in the question formulation.
Are A and B capacitors? Or to be treated as such?

 

[Apteronotus]

The objects represent two regions of a biological cell. Current in the form of ions is allowed to flow from one region to the other. Obviously when this current is allowed to flow, the potential difference between the two regions should decrease.

I was wondering if there are any equations which can describe this relation.

Stonebridge, you are right. If enough time is allowed to pass, then the potential difference would become zero.

 

[Stonebridge]

I know nothing about cell biology! I'm wondering, though, if it's asking a little too much to assume Ohm's Law is obeyed. Without that, it's not possible to quantify the current flow. And it's this current (I=V/R) which determines the rate at which the charge flows from from A to B.
Additionally, there is the relationship between the potential at A and B and the amount of charge localised at those points. (That's why I asked about capacitors).
In physics there is a formula for the discharge of a capacitor through a resistor.
V=Vo e^(-t/CR)
where Vo is initial potential difference, C is capacitance, R is resistance of circuit, t is time and V the pd across the capacitor at that time.
However, using something like this formula would be making a lot of assumptions about the way the cell behaves. What is R? What would C represent etc etc? I doubt it would work!
Maybe someone else with more knowledge of cell biology would like to try?

 

[diazona]

An exact formula would be pretty complicated, I'm sure (I don't know anything about cell biology either), but I would think that whatever it is, it'd still fit the general form of a decreasing curve that asymptotically approaches V=0. I doubt that the innards of a cell have complex electrical structures like transistors or diodes in them I wouldn't be that surprised if the exponential form
V = V_0 e^{-t/\tau}
turned out to be a pretty decent approximation, for some value of \tau which you'd probably have to determine empirically.

 

[vin300]

V = V_0 e^{-t/\tau}

How did you guess that?